Asymmetry and Persistence of Stock Returns: A Case of the Ghana Stock Exchange
|
|
- Jonah Potter
- 6 years ago
- Views:
Transcription
1 International Journal of Business and Economics Research 2016; 5(6): doi: /j.ijber ISSN: (Print); ISSN: X (Online) Asymmetry and Persistence of Stock Returns: A Case of the Ghana Stock Exchange Abonongo John 1, *, Oduro F. T. 1, Ackora-Prah J. 1, Luguterah Albert 2 1 College of Science, Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana 2 Faculty of Mathematical Sciences, Department of Statistics, University for Development Studies, Navrongo, Ghana address: abonongojohn@gmail.com (A. John) * Corresponding author To cite this article: Abonongo John, Oduro F. T, Ackora-Prah J., Luguterah Albert. Asymmetry and Persistence of Stock Returns: A Case of the Ghana Stock Exchange. International Journal of Business and Economics Research. Vol. 5, No. 6, 2016, pp doi: /j.ijber Received: May 19, 2016; Accepted: May 31, 2016; Published: November 11, 2016 Abstract: Measuring and estimating volatility of asset return is bubbly for risk management, asset allocation, and option pricing. This paper investigated the asymmetry and persistence of the return of some stocks on the Ghana Stock Exchange using univariate TGARCH-M (1, 1) and half-life measure of the daily returns of eight stocks from 02/01/2004 to 20/12/2014. It was realized that, volatility was persistent (explosive process) in all the stocks. The persistence in volatility was extended in investigating the half-life measure of the stocks and it was realized that almost all the stocks had strong mean reversion and short half-life measure with the exception of Fan Milk Limited. Also all the returns series exhibited a positive leverage effect parameter indicating that bad news influenced volatility than good news of the same magnitude. Keywords: Asymmetry, Persistent, Half-Life, Volatility, Leverage Effect 1. Introduction Stock price volatility is an extremely important concept in finance for numerous reasons. The literature on stock price volatility agrees on one key phenomenon. There is evidence of several movements in stock prices. In other words, dynamic nature of stock price behaviour is an accepted phenomenon and all participants in stock markets including regulators, professionals and academics have consensus about it. But, what causes stock price volatility is a question that remains unsettled in finance field. This is because of the great number of complicated variables, which is not an easy task and up to now there is no consensus about it. However researchers in quest of answers to this question have investigated the stock price volatility from different angles. In this regards, from late twentieth century and particularly after introducing ARCH model by [8], as said by [3] and [27], a lot of studies accomplished in developed country and to some extent in developing countries has been done by researchers in this area using different methods. [8] published a paper that measured the time-varying volatility. His model, ARCH, was based on the idea that a natural way to update a variance forecast is to average it with the most recent squared surprise (i.e. the squared deviation of the rate of return from its mean). While conventional time series and econometric models operate under an assumption of constant variance, the ARCH process allows the conditional variance to change over time as a function of past errors leaving the unconditional variance constant. [3] to overcome the ARCH limitations introduced his model, ARCH that generalized the ARCH model (GARCH) to allow for both a longer memory and a more flexible lag structure. As noted above, in the empirical application of the ARCH model, a relatively long lag in the conditional variance equation is often called for, and to avoid problems with negative variance parameters, a fixed lag structure is typically imposed. In the ARCH process the conditional variance is specified as a linear function of past sample variance only, whereas the GARCH process allows lagged conditional variances to enter in the model as well. [9] introduced the ARCH-M model by extending the ARCH model to allow the conditional variance to be determinant of the mean. Whereas in its standard form, ARCH model expresses the conditional variance as a linear function of past squared innovations, in this new model they hypothesized that,
2 184 Abonongo John et al.: Asymmetry and Persistence of Stock Returns: A Case of the Ghana Stock Exchange changing conditional variance directly affect the expected return on a portfolio. Their results from applying this model to three different data sets of bond yields are quite promising. Consequently, they concluded that risk premia are not time invariant; rather they vary systematically with agent s perceptions of underlying uncertainty. [24] extended the ARCH framework in order to better describe the behaviour of return volatilities. Nelson s study was important because of the fact that it extended the ARCH methodology in a new direction, breaking the rigidness of the G/ARCH specification. The most important contribution was to propose a model (Exponential Autoregressive Conditional Heteroskedasticity (EARCH)) to test the hypothesis that the variance of return was influenced differently by positive and negative excess returns. His study found that not only was the statement true, but also that excess returns were negatively related to stock market variance. [13] modified the primary restrictions of Generalized Autoregressive Conditional Heteroskedasticity- in Mean (GARCH-M) model based upon the truth that GARCH model enforce a symmetric response of volatility to positive and negative shocks, introduced the Glosten-Jagannathan- Runkle Generalized Autoregressive Conditional Heteroskedasticity (GJRGARCH) and the Threshold Generalized Autoregressive Conditional Heteroskedasticity (TGARCH) models. They concluded that there was a positive but significant relation between the conditional mean and conditional volatility of the excess return on stocks when the standard GARCH-M framework was used to model the stochastic volatility of stock returns. [10] measured the impact of bad and good news on volatility and reported an asymmetry in stock market volatility towards good news as compared to bad news. More specifically, market volatility was assumed to be associated with the arrival of news. A sudden drop in price was associated with bad news on the other hand, a sudden increase in price was said to be due to good news. They found that bad news created more volatility than good news of equal importance. This asymmetric characteristic of market volatility has come to be known as the leverage effect. In stock market, negative shocks lead to higher volatility than positive shocks. In case of commodity and energy returns, asymmetry is observed in opposite direction. Energy return volatility reacts more to positive shocks than to negative shocks. For studying asymmetry in crude oil volatility, [23] used exponential GARCH model to evaluate varying effects of positive and negative shocks on oil return volatility. [5] also studied the asymmetry effect on two crude oil prices; West Texas Intermediaries (WTI) and Brent crude oil. He found that volatility reacts more to negative shocks than to positive shocks. However, it was evident only for Brent crude not for WTI crude oil. The literature on asymmetry of energy prices is limited to crude oil prices. Persistence or long memory plays a crucial role in volatility forecasting and it has immense influence in risk management, derivative pricing and portfolio management. Persistence implies that any shocks to volatility do not die quickly rather its effect endures. Among the studies, [17], [26], [29] and [30] examined persistence in oil return volatility. [26] estimated volatility persistence of crude oil and natural gas using GARCH and half-life volatility measure and found the evidence of persistence in the volatility of crude oil and natural gas. However, his measure of persistence suggested that the fluctuations were short-lived than previously assumed. If there was a shock to crude oil or natural gas prices, it lasted up to 5 to 10 weeks. [1], estimated the daily returns of the Khartoum Stock Exchange using GARCH models. Their study showed that the conditional variance process was highly persistent and provided evidence on the existence of risk premium for the KSE index returns series. They also realised that, the asymmetric models provided better fit than the symmetric models which confirmed the existence of leverage effect. [28] also estimated persistence in crude oil and found the evidence of long memory even with structural break. Also, [14] estimated and compared the asymmetry and persistence of volatility of crude oil, natural gas and coal. Their research revealed that, coal volatility exhibited strong mean reversion whereas crude oil and natural gas return volatility endured shocks for relatively higher periods. And that volatility of crude oil and gas increased after positive shocks in price. [18] used Iterated Cumulative Sum of Squares (ICSS) to determine regime shifts and then applied in the asymmetric volatility models to study the impact of shocks on volatility persistence and asymmetry. Their results revealed that, the persistence and asymmetry in volatility were reduced considerably when regime shifts were taken into account in the models. [16] study in Nigeria obtained an evident of volatility clustering and volatility persistence and also asymmetric volatility effect in Nigeria. Moreover, [25] examined the behaviour of stock return volatility in the Kenyan stock exchange phases for the NSE20 share index and the 10 sample stocks over 11 years. They employed the FIEGARCH (1,d,1) in fitting the asymmetry effect and volatility persistent. Their results revealed persistent bullish phases than bearish with bear phases much frequent. Also, there was non-systematic pattern across all the stocks though a higher degree dependence in both the level and volatility in the bull periods and that, the FIEGARCH models was capable of modelling volatility clustering and asymmetry in volatility. The purpose of this paper is to investigate the asymmetry and persistence of some stocks on the Ghana Stock Exchange. This is to provide investors with information on how persistence some stocks are and their respective half-life measure so as make the right investment decisions. 2. Materials and Methods of Analysis 2.1. Source of Data This paper used secondary data of 8 stocks (CAL Bank Limited, Produce Buying Company, Fan Milk Limited, Clydestone (Ghana) Limited, Enterprise Group Limited,
3 International Journal of Business and Economics Research 2016; 5(6): Uniliver Ghana Limited, Tullow Oil Plc and Benso Oil Palm Plantation) from the Ghana Stock Exchange (GSE) and Annual Report Ghana databases comprising the daily closing prices from the period 02/01/2004 to 20/12/2014, totaling 7616 observations Methods of Data Analysis The daily closing prices were converted into compound returns given by; =log (1) where is the continuous compound returns at time, is the current closing stock price index at time and is the previous closing stock price index Tests Stationarity Test It is very paramount to establish the existence or nonexistence of unit root in the time series under study so as to be able to ascertain the nature of the process that produces the time series. This paper employed two quantitative unit root tests namely; the PhillipPerron (PP) unit root test and the Kwiatkowsky, Phillips, Schmidt and Shin (KPSS) test. The KPSS test was used to test the null hypothesis that the data generating process is stationary, H o : I(0) against the alternative that it is non-stationary, H 1 : I(1). This test was developed [19]. It assumes that there is no linear trend term and is given by; = +, 0 (2) where is a random walk, = + ; ~0, and is a white noise series. The previous pair of hypothesis is equivalent to;!: =0 : >0 If! is true, the model becomes =$%&'(&+ ; 0 hence is stationary. The test statistic is given by; *+,,= (3) 3 where 5 is the number of observations, 6 7 is an estimator of the long-run variance of the process. The PP statistic test the hypothesis; H o : unit root against H 1 : stationary about deterministic trend Under the H o of p = 0, the PP test Z p and Z τ statistics have the same asymptotic distributions as the ADF t-statistic and normalized bias statistics. The PP test is categorized into two statistics known as Phillips Z p and Z τ tests given by; =& <. =>? A,9 B (4) C =D E2 F,< GH.. 6 < =>? < 12 A,9 B GH.912 (5) 0 < J,9 = K 9 M4JN 2L.K MJ, for O=0, J,9 is a maximum likelihood estimate of the error terms J,9 is the covariance between the error terms j-periods apart for O>0. >? Q 9 =@6 A, J, when there exist no J4 J,9 autocorrelation between the error J,9 =0 for O>0, then >? 9 =@6 A, Jarque-Bera Test [15] is a goodness-of-fit test which examines if the sample data have kurtosis and skewness similar to a normal distribution. The test statistic is given by; RS=5.T U. V +WX. Y Z (6) where S and K are the sample skewness and kurtosis respectively. The Hypothesis is given by; H o : normality H 1 : non-normality If the sample data comes from a normal distribution JB should, asymptotically, have a chi-squared distribution with two degree of freedom Univariate Ljung-Box Test The [21] was employed to test whether there exist autocorrelation [ \ in the returns series. It is of the assumption that, the returns series and standardized residuals contain no serial correlation up to a given lag k. The statistic is given by; ]*=55+2 ` ^_. \4 (7) -\ where [ \ is the residual sample autocorrelation at lag a, T is the size of the series, k is the number of time lags included in the test. ]* has an approximately chi-square distribution with k degree of freedom. The null hypothesis is rejected and concluded at α-level of significance that, the residuals are free from serial correlation when the p- value is greater than the significance level Testing for ARCH Effects In fitting GARCH models, it is very essential to examine the residuals for evidence of ARCH effects. The observation that the magnitude of current residuals for any financial time series tends to be non-linearly related to the magnitude of their past residuals form the reasoning for ARCH test. This paper employed the ARCH-LM test as it is the most widely used method to test for ARCH effects in empirical studies ([6] and [22]). By representing the i lag autocorrelation of the squared or absolute returns by 2, L the Ljung-Box statistic is given by; c 6 ḃ -M ]=55+2 M4 ~d e (8)
4 186 Abonongo John et al.: Asymmetry and Persistence of Stock Returns: A Case of the Ghana Stock Exchange The LM hypothesis is given by;!: f =f = =f M =0 (no ARCH effect) against : f f f M 0 (ARCH effect) for at least i=1,2,..,j The statistic of the LM test is given by; kl=5.m ~d j (9) where j is the number of restrictions placed on the model, T is the total observations and m forms the regression The Durbin-Watson Test The [7] was employed to determine whether the error term in the mean equation follows an AR (1) process. The test requires the error term K to be distributed N (0, ) for the statistic to have an exact distribution. The test statistic is given as; n= < bp. o bo b. < bp o ḃ (10) where q M =r M r6 M and r M and r6 M are the observed and predicted values of the response variable for individual i respectively. n becomes smaller as the serial correlations increases. The hypothesis is given by;!: s=0 : s>0 Also, the n statistic can take on values between 0 and 4 and under the null hypothesis n is equal The Breusch-Godfrey Test This is also an LM test which was used to test for higherorder serial correlation in the disturbance. The test statistic is given by; S t =m (11) where N is the number of observations and m is the simple m from the regression u6 =@ u6 + +@ u6 +v w + +v`w` +K (12) The hypothesis is given by;!: &% (u%$%[[qa(i%& : (u%$%[[qa(i%& The test is asymptotically d (p) distributed The Mean Equation In modelling volatility, it is very essential to specify an appropriate mean equation. The mean equation should be white noise series, that is it should have a finite mean and variance; constant mean and variance, zero autocovariance, except at lag zero. Comparatively following [31] and [6], this paper employed the mean equation given by: =x+> +K (13) where X t is the returns for each stock, µ is a constant, λ is the coefficient of X t 1 and ε t is the innovation The Threshold GARCH-M (TGARCH-M) This model was proposed by [13] and [32]. It is simply a re-specification of the GARCH-M model with an additional term to account for asymmetry (leverage effect). In the general specification of this model, the TGARCH (p, q) model is given by; =f! + M4 f M +@ M n M K M + J4 v J J (14) where f! is a constant, n is the asymmetric component is the asymmetric coefficient. f M and v J are non-negative. Assuming the mean equation in Equation (13), the variance equation for TGARCH-M (1, 1) is given by; =f! +f K +@ n K +v (15) n =y 1 iz K <0, (n &q}' 0 iz K 0, %%n &q}' Q (16) then leverage effects exist in stock markets and 0 then the impact of news is asymmetric [12]. Also the model collapses to the standard GARCH form. Nevertheless, when the shock is positive (good news), the volatility is f, whereas if the news is negative (bad news), the effect on volatility is f +@. Similarly, is positive and statistically significant then negative shocks will have a larger effect on than positive shocks [4]. Also, since the conditional variance must be positive, the constraints of the parameters are f! >0, f 0, v 0 and f +@ 0. The model is stationary <21 f v Student-t Distributional Assumption The student-t distributional assumption was employed to account for fat tails that are common in most financial data. The ARCH models were estimated using the maximum likelihood approach given a distributional assumption. The contribution to the likelihood for observation t for the Student-t distribution is given by; a = log.. ƒ.. a% where Γ(.) is the gamma function and v > 2 is a shape parameter which controls the tail behaviour. When v the distribution converges to Gaussian distribution. N. ˆ log 1+= ŠB (17) Mean Reversion Mean reversion implies that current information have no
5 International Journal of Business and Economics Research 2016; 5(6): influence on the long run forecast of the volatility. Persistence dynamics in volatility is generally captured in the GARCH coefficient(s) of a stationary GARCH model. In stationary GARCH models, the volatility mean reverts to its long run level, at a rate given by the sum of ARCH and GARCH coefficients, which is usually close to one (1) for financial time series. The average number of time periods for the volatility to revert to its long run level is measured by the half-life of the volatility shock. The mean reverting form of the basic GARCH (1, 1) model is given by; K Œ =f +v K Œ + +v (18) where Œ Ž =, the unconditional long run level of volatility and X t = K Œ. The magnitude of the mean reverting rate f +v controls the speed of the mean reversion Half-Life One measure of volatility persistence is the volatility halflife τ, [11] defined half-life as the time required for the volatility to move half way back towards its unconditional mean. More precisely, τ is the smallest k such that N` Œ = N Œ (19) where k is the number of days, N` is the conditional expected value of volatility k days into the future and Œ is the unconditional long run level of volatility (the mean level to which the unconditional variance eventually reverts). Also, the GARCH (1, 1) process is mean reverting if (f +v ) < 1 since if this condition is satisfied, N` Œ as k. Thus, the forecast conditional variance reverts to the unconditional variance as the forecast horizon increases. For k 2 and a GARCH (1, 1) process, the value of N` is given by; N` =Œ +f +v ` N Œ, 2 (20) From Equation (19) and Equation (20), the number of days k for a GARCH (1, 1) process is given by; Œ +f +v ` N Œ Œ = N Œ (21) Therefore the half-life of a GARCH (1, 1) process is given by; = \! [ N /] \! N 3. Results and Discussion 3.1. Descriptive Statistics (22) Table 1 shows the summary statistics of the returns series. Most of the stocks had positive mean returns (CAL Bnak Limited, Fan Milk Limited,Enterprise Group Limited, Uniliver Ghana Limited, Tullow Oil Plc and Benso Oil Palm Plantation) ranging from to The rest of the stocks (Produce Buying Company and Clydestone (Ghana) Limited) had negative mean returns ranging from to The highest mean return was recorded in Benso Oil Palm Plantation (0.0020) and the lowest mean return recorded in Produce Buying Company ( ). A positive mean return indicates that investors of such stocks made gains whereas those with negative mean return shows that investors made losses. The standard deviation as a measure of risk was high in Tullow Oil Plc (0.0527) and low in Uniliver Ghana Limited (0.0187) indicating the risk levels across the stocks. The variability between risk and return as a measure of coefficient of variation ranges from (Clydestone (Ghana) Limited) to (Enterprise Group Limited). Also, most of the mean returns were positively skewed ranging from to This indicates that, the upper tail of the distribution of the return were ticker than the lower tail and that there were higher chances of gains than losses. That is, there was greater probability of making gains by investors in such stocks. Nevertheless, Enterprise Group Limited recorded a negative skewness ( ) indicating that there was a high probability of making loss than gain by investors. The excess kurtosis ranged from to which are greater than 3. This means that the underlying distribution of the returns are leptokurtic (highly peaked) in nature and heavy tailed and that there was more frequently extremely large deviations from the mean returns than a Gaussian distribution and hence making the stocks highly volatile. Table 1. Descriptive Statistics of the Returns Series. Stock Mean St. Dev CV Skewness Kurtosis CAL Bank Limited Produce Buying Company Fan Milk Limited Clydestone (Ghana) Limited Enterprise Group Limited Uniliver Ghana Limited Tullow Oil Plc Benso Oil Palm Plantation Further Analysis The PP and KPSS was employed in testing and confirming stationarity of the returns series. From Table 2, it is evident that for the PP tests, p values were very significant at 5% significance level and therefore the null hypothesis of non-
6 188 Abonongo John et al.: Asymmetry and Persistence of Stock Returns: A Case of the Ghana Stock Exchange stationary or unit root was rejected. In the case of the KPSS test, we failed to reject the null hypothesis of stationary since the test was significant at the 5% significance level. Table 2. PP Test and KPSS Test of the Returns Series. Therefore, the returns series were all stationary at the 5% level of significance. PP Test KPSS Test Stock Test Statistic P-value Test Statistic Critical value (5%) CAL Bank Limited ** Produce Buying Company ** Fan Milk Limited ** Clydestone (Ghana) Limited ** Enterprise Group Limited ** Uniliver Ghana Limited ** Tullow Oil Plc ** Benso Oil Palm Plantation ** ** Significant at 5% significance level. The residuals of the individual equations were examined for the presence or absence of conditional heteroskedasticity. The ARCH-LM test was conducted at lags 1, 7 and 14. It is evident from Table 3 that all the returns series exhibited ARCH effects at the 5% significance level. Table 3. ARCH-LM Test of the Selected Returns Series. Stock Lag Test Statistic P-value ** CAL Bank Limited ** ** ** Produce Buying Company ** ** ** Fan Milk Limited ** ** ** Clydestone (Ghana) Limited ** ** ** Enterprise Group Limited ** ** ** Uniliver Ghana Limited ** ** ** Tullow Oil Plc ** ** ** Benso Oil Palm Plantation ** ** ** Significant at 5% significance level The returns series were tested for normality, autocorrelation and heteroskedasticity using the Jarque-Bera and Ljung Box tests respectively. It is evident from Table 4 that, the Jarque-Bera test for normality was significant at the 5% significance level, therefore we concluded that the returns series are not normally distributed. The LB(14) and LB 2 (14) are all significant at the 5% level of significance. We therefore reject the null hypothesis of no autocorrelation in the levels of the returns series. The significance of LB 2 (14) statistic suggest the presence of ARCH effects and hence making an AR(1) conditional mean model more suitable for GARCH specification and it also indicates the presence of volatility clustering. Table 4. Test for Normality, Autocorrelation and Heteroscedascitity of Return Series. Stock Jarque-Bera LB(14) LB 2 (14) CAL Bank Limited * * * Produce Buying Company * * * Fan Milk Limited * * * Clydestone (Ghana) Limited * * * Enterprise Group Limited * * * Uniliver Ghana Limited * * * Tullow Oil Plc * * * Benso Oil Palm Plantation * * * *Significant at 5% significance level. From Table 5, it is evident that the DW-AR(1) had indications of autocorrelation but the B-G AR(1) indicated no evidence of autocorrelation since it was not significant at the 5% level of significance across the entire returns series, therefore, we fail to reject the null hypothesis of no autocorrelation. Thus, making the choice of mean equation more appropriate for the GARCH estimation. Table 5. Mean Equation Results for the Returns Series. Stock DW-AR(1) B-G(1) ARCHLM AR(1) CAL Bank Limited * Produce Buying Company * Fan Milk Limited * Clydestone (Ghana) limited * Enterprise Group Limited * Uniliver Ghana Limited * Tullow Oil Plc * Benso Oil Palm Plantation * *Significant at 5% significance level. The TGARCH was investigated for stationarity by summing the ARCH (α) and GARCH (β) coefficients. As it was reported in Table 6, all the estimated models were stationary indicating that the TGARCH was appropriate for asymmetric modelling of volatility. Again, the summation of the ARCH and GARCH coefficients was extended in measuring the level of persistence. It was evident that, the summation of α and β were all closer to one (1) indicating their persistence levels. Fan Milk Limited exhibited the
7 International Journal of Business and Economics Research 2016; 5(6): highest level of persistence (0.9622) with the least persistence (0.7580) level recorded in Produce Buying Company. Also, the TGARCH was extended in examining the leverage effect parameter γ, it was evident the leverage effect parameter across all the returns series were positive and significant at the 5% significance level. This means that there was the probability of bad news influencing volatility than good news of the same magnitude hence making volatility across the stocks to be asymmetric in nature. All the models were tested for ARCH effects and it was clear that the ARCH-LM test was not significant at the 5% level of significance hence there was no further ARCH effects. Table 6. Estimated TGARCH-M (1,1) Model. Stock + š ARCHLM CAL Bank Limited * Produce Buying Company * Fan Milk Limited * Clydestone (Ghana) Limited * Enterprise Group Limited * Uniliver Ghana Limited * Tullow Oil Plc * Benso Oil Palm Plantation * * Significant at 5% significance level. The persistence and half-life measure of volatility of the returns series were investigated from the TGARCH-M (1,1) model. The summation of α and β was used and it is evident from Table 7, all the 8 returns series were persistent exhibiting long-memory since their summation of α and β were closer to one (1). Also, in terms of mean reversion, almost all the returns series have strong mean reversion with the exception of Fan Milk Limited. Fan Milk Limited exhibited the highest persistence level. The half-life measure of volatility also revealed the same trend. The half-life of most of returns series were short (CAL Bank Limited (6 days), Produce Buying Company (4 days), Clydeston (Ghana) Limited (5 days), Enterprise Group Limited (7 days), Uniliver Ghana Limited (4 days), Tullow Oil Limited (5 days) and Benso Oil Palm Plantation (4 days)) with the exception of Fan Milk Limited (19 days). It was also clear that, once the returns series were less persistent, their halflife measure of volatility tends to be short. The persistence and half-life in volatility showed that all the eight returns series exhibited some level of volatility persistence. This degree of persistence was extended in measuring the half-life in volatility. Stocks that exhibited high degree of persistence imply their volatility will not move quickly to their long-run volatility levels whereas those with less degree of persistence will have their volatility moving very quickly to their longrun volatility levels. That is, there is the expectation that stocks with high degree of persistence will have high half-life and weak mean reversion whereas those with low persistence will have low half-life and strong mean reversion. The implication of weak and strong mean reversion is that, for stocks with strong mean reversion means that, the returns of those stocks approaches their average volatility very quickly whereas for stocks with weak mean reversion, their returns takes a long period to return towards their average volatility. Therefore, the results showed that, Produce Buying Company, Uniliver Ghana Limited and Benso Oil Palm Plantation had strong mean reversion since they all had their half-life measure been four (4 days). This means that, any shock to any of these stocks take 4 days to return half-way back without any further volatility (i.e. a shock takes 4 days to return half-way back to its volatility). Also, CAL Bank Limited, Clydestone, Enterprise Group and Tullow Oil Plc have strong mean reversion since the half-life measure were 6 days, 5 days, 7 days and 5 days respectively. This implies that a shock to CAL Bank Limited will take 6 days to return half-way back to its volatility, a shock to Clydestone (Ghana) Limited will take 5 days to revert, any shock to Enterprise Group Limited and Tullow will take 7 days and 5 days respectively to return half-way back without any further volatility. The half-life measure of Fan Milk Limited was 19 days indicating that any shock to Fan Milk Limited will take 19 days to mean revert. This implies that, investors will prefer stocks that have strong mean reversion since their volatility does not stay for a long time. But in the situation where positive shocks increases volatility, investors will prefer to invest in stocks that have high persistence measure of volatility and weak mean reversion. Also in a market where risk is priced, investors will prefer investing in stocks with high half-life measure since at the end of the day their returns will match the risk taken. Table 7. Persistence and Half-life Volatility measure of the Returns Series. Stock α + β CAL Bank Limited Produce Buying Company Fan Milk Limited Clydestone (Ghana) Limited Enterprise Group Limited Uniliver Ghana Limited Tullow Oil Plc Benso Oil Palm Plantation Conclusion Half-life volatility measure (days) This paper examined the asymmetry and persistence in stock returns using univariate TGARCH-M (1,1) with the student-t distributional assumption and half-life measure. From the results, it was evident that volatility was persistent across all the stocks since the summation of ARCH and GARCH coefficients were all very close to one (1). The persistence and half-life measure revealed that, all the stocks exhibited some level of persistence in them and strong mean reversion. Fan Milk Limited was highly persistent with a weak mean reversion and a half-life of 19 days as compared to CAL Bank Limited, Produce Buying Company, Enterprise Group Limited, Uniliver Ghana Limited, Tullow Oil Plc and Benso Oil Palm Plantation which had 5 days, 7 days, 4 days, 5 days and 4 days respectively. Also all the returns series
8 190 Abonongo John et al.: Asymmetry and Persistence of Stock Returns: A Case of the Ghana Stock Exchange exhibited positive leverage effect parameter indicating that bad news influenced volatility than good news of the same magnitude and hence making volatility asymmetric. References [1] Ahmed, E. and Suliman, Z. (2011). Stock market volatility using garch models: Evidence from sudan. International Journal of Business and Social Science, 2(23): [2] Banerjee, A. and Sarkar, S. (2006). Modelling daily volatility of the indian stock market using intra-day data. IIM CALCUTTA, Working paper. [3] Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity, north holland. Journal of Econometrics, 31(3): [4] Cater, R., Hill, E., and William, C. (2007). Principles of Econometrics, 3rd Edition New York. John Wiley and Sons, Inc. [5] Cheong, C. (2009). Modelling and forecasting crude oil markets using arch-type models. Energy Policy, 37(6): [6] Chinzara, Z. and Aziakpono, M. (2009). Dynamic rreturn linkages and volatility transmission between south aafrica and world major stock markets. Studies in Economics and Econometrics, 33(3): [7] Durbin, J. and Watson, G. (1950). Testing for serial correlation in least square regression. Econometrica, 37: [8] Engle, R. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of the united kingdom inflation. Econometrica, 50: [9] Engle, R., Lilien, D., and Robins, R. (1987). Estimating time varying risk premia in the term structure, the arch-m model. Econometrica, 55(2): [10] Engle, R. and Ng, V. (1993). Measuring and testing the impact of news on volatility. Journal of Finance, 48: [11] Engle, R. and Patton, A. (2001). What good is a volatility model? Quantitative Finance, 1(2): [12] Eview, M. (2007). Help system. [13] Glosten, L., Jagannathan, R., and Runkle, D. (1993). On the relation between expected value and the volatility of the nominal excess return on stocks. Journal of Finance, 48: [14] Hasan, M., Selin, A., and Fazle, R. (2013). Asymmetry and persistence of energy price volatility. International Journal of Finance and Accounting, 2(7): [15] Jarque, C. and Bera, A. (1987). A test of nornormal of observations and regression residuals. International Statistical Review, 55: Volatility in Nigerian Stock Exchange. Journal of Business and Management 4(12): [17] Kang, S., Kang, M., and Yoon, M. (2009). Forecasting oil price volatility. Energy Economics, 31(1): [18] Kumar, D. and Maheswaran S. (2012). Modelling asymmetry and persistence under the impact of sudden changes in the volatility of the Indian stock market. IIMB Management Review, 24(3): [19] Kwiatkowsky, D., Phillips, P., P., and Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54(13): [20] Lee, J. and King, M. (1993). A locally most powerful based score test for arch and garch regression distrubances. Journal of Business and Economic Statistics, 7: [21] Ljung, G. and Box, G. (1978). On the measure of lack of fit in time series models. Econometrica, 65(2): [22] Magnus, F. and Fosu, O. (2006). Modelling and forecasting volatility of returns on the ghana stock exchange using garch models. American Journal of Applied Science, 3(10): [23] Narayan, P. and Narayan, S. (2007). Modelling oil price volatility. Energy Policy, 35(12): [24] Nelson, D. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59(2): [25] Ogega H. O and Freshia M. W (2016). Analysis of Asymmetric and Persistence in Stock Return Volatility in the Nairobi Security Exchange Market Phases. Journal of Finance and Economics, 4(3): [26] Pindyck, R. (2004). Volatility in natural gas and oil markets. Journal of Energy and Development, 30(1):1 19. [27] Poon and Granger (2003). Forecasting volatility in financial markets. Journal of Economic Literature, 41: [28] Salisu, A. and Fasanya, I. (2013). Modelling oil price volatility with structural breaks. Energy Policy, 52(2): [29] Serletis, A. and Andreadis, I. (2004). Random fractal structures in north american energy markets. Energy Economics, 26(3): [30] Tabak, B. and Cajueiro, D. (2007). Are markets oil markets becoming weakly efficient over time? a test for time-varying long-rang dependence in price and volatility. Energy Economics, 29(1): [31] Takaendesa, P., Tsheole, P., and Aziakpono, M. (2006). Real exchange rate volatility and its effect on trade flows. new evidence from south africa. Studies in Economics and Econometrics, 30(3): [32] Zakoian, J. (1994). Threshold heteroscedastic models. Journal of Economics Dynamics and Control, 18: [16] Kalu, E. and Friday A. S (2012). Modelling Asymmetry
Modelling Stock Market Return Volatility: Evidence from India
Modelling Stock Market Return Volatility: Evidence from India Saurabh Singh Assistant Professor, Graduate School of Business,Devi Ahilya Vishwavidyalaya, Indore 452001 (M.P.) India Dr. L.K Tripathi Dean,
More informationResearch Article The Volatility of the Index of Shanghai Stock Market Research Based on ARCH and Its Extended Forms
Discrete Dynamics in Nature and Society Volume 2009, Article ID 743685, 9 pages doi:10.1155/2009/743685 Research Article The Volatility of the Index of Shanghai Stock Market Research Based on ARCH and
More informationVolatility Analysis of Nepalese Stock Market
The Journal of Nepalese Business Studies Vol. V No. 1 Dec. 008 Volatility Analysis of Nepalese Stock Market Surya Bahadur G.C. Abstract Modeling and forecasting volatility of capital markets has been important
More informationVolatility Clustering of Fine Wine Prices assuming Different Distributions
Volatility Clustering of Fine Wine Prices assuming Different Distributions Cynthia Royal Tori, PhD Valdosta State University Langdale College of Business 1500 N. Patterson Street, Valdosta, GA USA 31698
More informationIndian Institute of Management Calcutta. Working Paper Series. WPS No. 797 March Implied Volatility and Predictability of GARCH Models
Indian Institute of Management Calcutta Working Paper Series WPS No. 797 March 2017 Implied Volatility and Predictability of GARCH Models Vivek Rajvanshi Assistant Professor, Indian Institute of Management
More informationAmath 546/Econ 589 Univariate GARCH Models: Advanced Topics
Amath 546/Econ 589 Univariate GARCH Models: Advanced Topics Eric Zivot April 29, 2013 Lecture Outline The Leverage Effect Asymmetric GARCH Models Forecasts from Asymmetric GARCH Models GARCH Models with
More informationInternational Journal of Business and Administration Research Review. Vol.3, Issue.22, April-June Page 1
A STUDY ON ANALYZING VOLATILITY OF GOLD PRICE IN INDIA Mr. Arun Kumar D C* Dr. P.V.Raveendra** *Research scholar,bharathiar University, Coimbatore. **Professor and Head Department of Management Studies,
More informationModelling Stock Returns Volatility on Uganda Securities Exchange
Applied Mathematical Sciences, Vol. 8, 2014, no. 104, 5173-5184 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.46394 Modelling Stock Returns Volatility on Uganda Securities Exchange Jalira
More informationModeling Exchange Rate Volatility using APARCH Models
96 TUTA/IOE/PCU Journal of the Institute of Engineering, 2018, 14(1): 96-106 TUTA/IOE/PCU Printed in Nepal Carolyn Ogutu 1, Betuel Canhanga 2, Pitos Biganda 3 1 School of Mathematics, University of Nairobi,
More informationOil Price Effects on Exchange Rate and Price Level: The Case of South Korea
Oil Price Effects on Exchange Rate and Price Level: The Case of South Korea Mirzosaid SULTONOV 東北公益文科大学総合研究論集第 34 号抜刷 2018 年 7 月 30 日発行 研究論文 Oil Price Effects on Exchange Rate and Price Level: The Case
More informationMODELING EXCHANGE RATE VOLATILITY OF UZBEK SUM BY USING ARCH FAMILY MODELS
International Journal of Economics, Commerce and Management United Kingdom Vol. VI, Issue 11, November 2018 http://ijecm.co.uk/ ISSN 2348 0386 MODELING EXCHANGE RATE VOLATILITY OF UZBEK SUM BY USING ARCH
More informationThe Great Moderation Flattens Fat Tails: Disappearing Leptokurtosis
The Great Moderation Flattens Fat Tails: Disappearing Leptokurtosis WenShwo Fang Department of Economics Feng Chia University 100 WenHwa Road, Taichung, TAIWAN Stephen M. Miller* College of Business University
More informationA Study on the Performance of Symmetric and Asymmetric GARCH Models in Estimating Stock Returns Volatility
Vol., No. 4, 014, 18-19 A Study on the Performance of Symmetric and Asymmetric GARCH Models in Estimating Stock Returns Volatility Mohd Aminul Islam 1 Abstract In this paper we aim to test the usefulness
More informationVolatility in the Indian Financial Market Before, During and After the Global Financial Crisis
Volatility in the Indian Financial Market Before, During and After the Global Financial Crisis Praveen Kulshreshtha Indian Institute of Technology Kanpur, India Aakriti Mittal Indian Institute of Technology
More informationSt. Theresa Journal of Humanities and Social Sciences
Volatility Modeling for SENSEX using ARCH Family G. Arivalagan* Research scholar, Alagappa Institute of Management Alagappa University, Karaikudi-630003, India. E-mail: arivu760@gmail.com *Corresponding
More informationChapter 4 Level of Volatility in the Indian Stock Market
Chapter 4 Level of Volatility in the Indian Stock Market Measurement of volatility is an important issue in financial econometrics. The main reason for the prominent role that volatility plays in financial
More informationA Study of Stock Return Distributions of Leading Indian Bank s
Global Journal of Management and Business Studies. ISSN 2248-9878 Volume 3, Number 3 (2013), pp. 271-276 Research India Publications http://www.ripublication.com/gjmbs.htm A Study of Stock Return Distributions
More informationConditional Heteroscedasticity
1 Conditional Heteroscedasticity May 30, 2010 Junhui Qian 1 Introduction ARMA(p,q) models dictate that the conditional mean of a time series depends on past observations of the time series and the past
More informationAn Empirical Research on Chinese Stock Market Volatility Based. on Garch
Volume 04 - Issue 07 July 2018 PP. 15-23 An Empirical Research on Chinese Stock Market Volatility Based on Garch Ya Qian Zhu 1, Wen huili* 1 (Department of Mathematics and Finance, Hunan University of
More informationARCH and GARCH models
ARCH and GARCH models Fulvio Corsi SNS Pisa 5 Dic 2011 Fulvio Corsi ARCH and () GARCH models SNS Pisa 5 Dic 2011 1 / 21 Asset prices S&P 500 index from 1982 to 2009 1600 1400 1200 1000 800 600 400 200
More informationModeling the volatility of FTSE All Share Index Returns
MPRA Munich Personal RePEc Archive Modeling the volatility of FTSE All Share Index Returns Bayraci, Selcuk University of Exeter, Yeditepe University 27. April 2007 Online at http://mpra.ub.uni-muenchen.de/28095/
More informationFinancial Time Series Analysis (FTSA)
Financial Time Series Analysis (FTSA) Lecture 6: Conditional Heteroscedastic Models Few models are capable of generating the type of ARCH one sees in the data.... Most of these studies are best summarized
More informationFinancial Econometrics
Financial Econometrics Volatility Gerald P. Dwyer Trinity College, Dublin January 2013 GPD (TCD) Volatility 01/13 1 / 37 Squared log returns for CRSP daily GPD (TCD) Volatility 01/13 2 / 37 Absolute value
More informationESTABLISHING WHICH ARCH FAMILY MODEL COULD BEST EXPLAIN VOLATILITY OF SHORT TERM INTEREST RATES IN KENYA.
ESTABLISHING WHICH ARCH FAMILY MODEL COULD BEST EXPLAIN VOLATILITY OF SHORT TERM INTEREST RATES IN KENYA. Kweyu Suleiman Department of Economics and Banking, Dokuz Eylul University, Turkey ABSTRACT The
More informationApplication of Conditional Autoregressive Value at Risk Model to Kenyan Stocks: A Comparative Study
American Journal of Theoretical and Applied Statistics 2017; 6(3): 150-155 http://www.sciencepublishinggroup.com/j/ajtas doi: 10.11648/j.ajtas.20170603.13 ISSN: 2326-8999 (Print); ISSN: 2326-9006 (Online)
More informationModeling Volatility of Price of Some Selected Agricultural Products in Ethiopia: ARIMA-GARCH Applications
Modeling Volatility of Price of Some Selected Agricultural Products in Ethiopia: ARIMA-GARCH Applications Background: Agricultural products market policies in Ethiopia have undergone dramatic changes over
More informationDeterminants of Stock Prices in Ghana
Current Research Journal of Economic Theory 5(4): 66-7, 213 ISSN: 242-4841, e-issn: 242-485X Maxwell Scientific Organization, 213 Submitted: November 8, 212 Accepted: December 21, 212 Published: December
More informationForecasting Volatility of USD/MUR Exchange Rate using a GARCH (1,1) model with GED and Student s-t errors
UNIVERSITY OF MAURITIUS RESEARCH JOURNAL Volume 17 2011 University of Mauritius, Réduit, Mauritius Research Week 2009/2010 Forecasting Volatility of USD/MUR Exchange Rate using a GARCH (1,1) model with
More informationModelling Stock Returns Volatility In Nigeria Using GARCH Models
MPRA Munich Personal RePEc Archive Modelling Stock Returns Volatility In Nigeria Using GARCH Models Kalu O. Emenike Dept. of Banking and Finance, University of Nigeria Enugu Campus,Enugu State Nigeria
More informationPrerequisites for modeling price and return data series for the Bucharest Stock Exchange
Theoretical and Applied Economics Volume XX (2013), No. 11(588), pp. 117-126 Prerequisites for modeling price and return data series for the Bucharest Stock Exchange Andrei TINCA The Bucharest University
More informationModelling and Forecasting Volatility of Returns on the Ghana Stock Exchange Using GARCH Models
MPRA Munich Personal RePEc Archive Modelling and Forecasting Volatility of Returns on the Ghana Stock Exchange Using GARCH Models Joseph Magnus Frimpong and Eric Fosu Oteng-Abayie 7. October 2006 Online
More informationDATABASE AND RESEARCH METHODOLOGY
CHAPTER III DATABASE AND RESEARCH METHODOLOGY The nature of the present study Direct Tax Reforms in India: A Comparative Study of Pre and Post-liberalization periods is such that it requires secondary
More informationImplied Volatility v/s Realized Volatility: A Forecasting Dimension
4 Implied Volatility v/s Realized Volatility: A Forecasting Dimension 4.1 Introduction Modelling and predicting financial market volatility has played an important role for market participants as it enables
More informationThe Impact of Falling Crude Oil Price on Financial Markets of Advanced East Asian Countries
10 Journal of Reviews on Global Economics, 2018, 7, 10-20 The Impact of Falling Crude Oil Price on Financial Markets of Advanced East Asian Countries Mirzosaid Sultonov * Tohoku University of Community
More informationModelling Volatility of the Market Returns of Jordanian Banks: Empirical Evidence Using GARCH framework
(GJEB) 1 (1) (2016) 1-14 Science Reflection (GJEB) Website: http:// Modelling Volatility of the Market Returns of Jordanian Banks: Empirical Evidence Using GARCH framework 1 Hamed Ahmad Almahadin, 2 Gulcay
More informationRecent analysis of the leverage effect for the main index on the Warsaw Stock Exchange
Recent analysis of the leverage effect for the main index on the Warsaw Stock Exchange Krzysztof Drachal Abstract In this paper we examine four asymmetric GARCH type models and one (basic) symmetric GARCH
More informationStudy on Dynamic Risk Measurement Based on ARMA-GJR-AL Model
Applied and Computational Mathematics 5; 4(3): 6- Published online April 3, 5 (http://www.sciencepublishinggroup.com/j/acm) doi:.648/j.acm.543.3 ISSN: 38-565 (Print); ISSN: 38-563 (Online) Study on Dynamic
More informationA market risk model for asymmetric distributed series of return
University of Wollongong Research Online University of Wollongong in Dubai - Papers University of Wollongong in Dubai 2012 A market risk model for asymmetric distributed series of return Kostas Giannopoulos
More informationForecasting the Volatility in Financial Assets using Conditional Variance Models
LUND UNIVERSITY MASTER S THESIS Forecasting the Volatility in Financial Assets using Conditional Variance Models Authors: Hugo Hultman Jesper Swanson Supervisor: Dag Rydorff DEPARTMENT OF ECONOMICS SEMINAR
More informationEstimating and forecasting volatility of stock indices using asymmetric GARCH models and Student-t densities: Evidence from Chittagong Stock Exchange
IJBFMR 3 (215) 19-34 ISSN 253-1842 Estimating and forecasting volatility of stock indices using asymmetric GARCH models and Student-t densities: Evidence from Chittagong Stock Exchange Md. Qamruzzaman
More informationRETURNS AND VOLATILITY SPILLOVERS IN BRIC (BRAZIL, RUSSIA, INDIA, CHINA), EUROPE AND USA
RETURNS AND VOLATILITY SPILLOVERS IN BRIC (BRAZIL, RUSSIA, INDIA, CHINA), EUROPE AND USA Burhan F. Yavas, College of Business Administrations and Public Policy California State University Dominguez Hills
More informationModelling Inflation Uncertainty Using EGARCH: An Application to Turkey
Modelling Inflation Uncertainty Using EGARCH: An Application to Turkey By Hakan Berument, Kivilcim Metin-Ozcan and Bilin Neyapti * Bilkent University, Department of Economics 06533 Bilkent Ankara, Turkey
More informationIntaz Ali & Alfina Khatun Talukdar Department of Economics, Assam University
Available online at http://sijournals.com/ijae/ ISSN: 2345-5721 Stock Market Volatility and Returns: A Study of National Stock Exchange in India Intaz Ali & Alfina Khatun Talukdar Department of Economics,
More informationAsian Economic and Financial Review A REGRESSION BASED APPROACH TO CAPTURING THE LEVEL DEPENDENCE IN THE VOLATILITY OF STOCK RETURNS
Asian Economic and Financial Review ISSN(e): 2222-6737/ISSN(p): 2305-2147 URL: www.aessweb.com A REGRESSION BASED APPROACH TO CAPTURING THE LEVEL DEPENDENCE IN THE VOLATILITY OF STOCK RETURNS Lakshmi Padmakumari
More informationAssicurazioni Generali: An Option Pricing Case with NAGARCH
Assicurazioni Generali: An Option Pricing Case with NAGARCH Assicurazioni Generali: Business Snapshot Find our latest analyses and trade ideas on bsic.it Assicurazioni Generali SpA is an Italy-based insurance
More informationMODELING VOLATILITY OF BSE SECTORAL INDICES
MODELING VOLATILITY OF BSE SECTORAL INDICES DR.S.MOHANDASS *; MRS.P.RENUKADEVI ** * DIRECTOR, DEPARTMENT OF MANAGEMENT SCIENCES, SVS INSTITUTE OF MANAGEMENT SCIENCES, MYLERIPALAYAM POST, ARASAMPALAYAM,COIMBATORE
More informationMeasuring the Systematic Risk of Stocks Using the Capital Asset Pricing Model
Journal of Investment and Management 2017; 6(1): 13-21 http://www.sciencepublishinggroup.com/j/jim doi: 10.11648/j.jim.20170601.13 ISSN: 2328-7713 (Print); ISSN: 2328-7721 (Online) Measuring the Systematic
More informationStock Price Volatility in European & Indian Capital Market: Post-Finance Crisis
International Review of Business and Finance ISSN 0976-5891 Volume 9, Number 1 (2017), pp. 45-55 Research India Publications http://www.ripublication.com Stock Price Volatility in European & Indian Capital
More informationSelection of Stocks on the Ghana Stock Exchange Using Principal Component Analysis
International Journal of Theoretical and Applied Mathematics 2016; 2(2): 100-109 http://www.sciencepublishinggroup.com/j/ijtam doi: 10.11648/j.ijtam.20160202.21 Selection of Stocks on the Ghana Stock Exchange
More informationDemand For Life Insurance Products In The Upper East Region Of Ghana
Demand For Products In The Upper East Region Of Ghana Abonongo John Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana Luguterah Albert Department of Statistics,
More informationModelling the Stock Price Volatility Using Asymmetry Garch and Ann-Asymmetry Garch Models
International Journal of Data Science and Analysis 218; 4(4): 46-52 http://www.sciencepublishinggroup.com/j/ijdsa doi: 1.11648/j.ijdsa.21844.11 ISSN: 2575-1883 (Print); ISSN: 2575-1891 (Online) Modelling
More informationLecture 5: Univariate Volatility
Lecture 5: Univariate Volatility Modellig, ARCH and GARCH Prof. Massimo Guidolin 20192 Financial Econometrics Spring 2015 Overview Stepwise Distribution Modeling Approach Three Key Facts to Remember Volatility
More informationMODELING ROMANIAN EXCHANGE RATE EVOLUTION WITH GARCH, TGARCH, GARCH- IN MEAN MODELS
MODELING ROMANIAN EXCHANGE RATE EVOLUTION WITH GARCH, TGARCH, GARCH- IN MEAN MODELS Trenca Ioan Babes-Bolyai University, Faculty of Economics and Business Administration Cociuba Mihail Ioan Babes-Bolyai
More informationForecasting Stock Index Futures Price Volatility: Linear vs. Nonlinear Models
The Financial Review 37 (2002) 93--104 Forecasting Stock Index Futures Price Volatility: Linear vs. Nonlinear Models Mohammad Najand Old Dominion University Abstract The study examines the relative ability
More informationINFORMATION EFFICIENCY HYPOTHESIS THE FINANCIAL VOLATILITY IN THE CZECH REPUBLIC CASE
INFORMATION EFFICIENCY HYPOTHESIS THE FINANCIAL VOLATILITY IN THE CZECH REPUBLIC CASE Abstract Petr Makovský If there is any market which is said to be effective, this is the the FOREX market. Here we
More informationResearch on the GARCH model of the Shanghai Securities Composite Index
International Academic Workshop on Social Science (IAW-SC 213) Research on the GARCH model of the Shanghai Securities Composite Index Dancheng Luo Yaqi Xue School of Economics Shenyang University of Technology
More informationBESSH-16. FULL PAPER PROCEEDING Multidisciplinary Studies Available online at
FULL PAPER PROEEDING Multidisciplinary Studies Available online at www.academicfora.com Full Paper Proceeding BESSH-2016, Vol. 76- Issue.3, 15-23 ISBN 978-969-670-180-4 BESSH-16 A STUDY ON THE OMPARATIVE
More informationLecture 5a: ARCH Models
Lecture 5a: ARCH Models 1 2 Big Picture 1. We use ARMA model for the conditional mean 2. We use ARCH model for the conditional variance 3. ARMA and ARCH model can be used together to describe both conditional
More informationModelling Kenyan Foreign Exchange Risk Using Asymmetry Garch Models and Extreme Value Theory Approaches
International Journal of Data Science and Analysis 2018; 4(3): 38-45 http://www.sciencepublishinggroup.com/j/ijdsa doi: 10.11648/j.ijdsa.20180403.11 ISSN: 2575-1883 (Print); ISSN: 2575-1891 (Online) Modelling
More informationVolatility of the Banking Sector Stock Returns in Nigeria
Ruhuna Journal of Management and Finance Volume 1 Number 1 - January 014 ISSN 35-9 R JMF Volatility of the Banking Sector Stock Returns in Nigeria K.O. Emenike and W.U. Ani K.O. Emenike * and W.U. Ani
More informationInvestment Opportunity in BSE-SENSEX: A study based on asymmetric GARCH model
Investment Opportunity in BSE-SENSEX: A study based on asymmetric GARCH model Jatin Trivedi Associate Professor, Ph.D AMITY UNIVERSITY, Mumbai contact.tjatin@gmail.com Abstract This article aims to focus
More informationFinancial Econometrics Jeffrey R. Russell. Midterm 2014 Suggested Solutions. TA: B. B. Deng
Financial Econometrics Jeffrey R. Russell Midterm 2014 Suggested Solutions TA: B. B. Deng Unless otherwise stated, e t is iid N(0,s 2 ) 1. (12 points) Consider the three series y1, y2, y3, and y4. Match
More informationThe University of Chicago, Booth School of Business Business 41202, Spring Quarter 2009, Mr. Ruey S. Tsay. Solutions to Final Exam
The University of Chicago, Booth School of Business Business 41202, Spring Quarter 2009, Mr. Ruey S. Tsay Solutions to Final Exam Problem A: (42 pts) Answer briefly the following questions. 1. Questions
More informationInflation and inflation uncertainty in Argentina,
U.S. Department of the Treasury From the SelectedWorks of John Thornton March, 2008 Inflation and inflation uncertainty in Argentina, 1810 2005 John Thornton Available at: https://works.bepress.com/john_thornton/10/
More informationCross-Sectional Distribution of GARCH Coefficients across S&P 500 Constituents : Time-Variation over the Period
Cahier de recherche/working Paper 13-13 Cross-Sectional Distribution of GARCH Coefficients across S&P 500 Constituents : Time-Variation over the Period 2000-2012 David Ardia Lennart F. Hoogerheide Mai/May
More informationRISK SPILLOVER EFFECTS IN THE CZECH FINANCIAL MARKET
RISK SPILLOVER EFFECTS IN THE CZECH FINANCIAL MARKET Vít Pošta Abstract The paper focuses on the assessment of the evolution of risk in three segments of the Czech financial market: capital market, money/debt
More informationThe Effect of 9/11 on the Stock Market Volatility Dynamics: Empirical Evidence from a Front Line State
Aalborg University From the SelectedWorks of Omar Farooq 2008 The Effect of 9/11 on the Stock Market Volatility Dynamics: Empirical Evidence from a Front Line State Omar Farooq Sheraz Ahmed Available at:
More informationGARCH Models for Inflation Volatility in Oman
Rev. Integr. Bus. Econ. Res. Vol 2(2) 1 GARCH Models for Inflation Volatility in Oman Muhammad Idrees Ahmad Department of Mathematics and Statistics, College of Science, Sultan Qaboos Universty, Alkhod,
More informationApplying asymmetric GARCH models on developed capital markets :An empirical case study on French stock exchange
Applying asymmetric GARCH models on developed capital markets :An empirical case study on French stock exchange Jatin Trivedi, PhD Associate Professor at International School of Business & Media, Pune,
More informationForecasting Volatility in the Chinese Stock Market under Model Uncertainty 1
Forecasting Volatility in the Chinese Stock Market under Model Uncertainty 1 Yong Li 1, Wei-Ping Huang, Jie Zhang 3 (1,. Sun Yat-Sen University Business, Sun Yat-Sen University, Guangzhou, 51075,China)
More informationEmpirical Analysis of Stock Return Volatility with Regime Change: The Case of Vietnam Stock Market
7/8/1 1 Empirical Analysis of Stock Return Volatility with Regime Change: The Case of Vietnam Stock Market Vietnam Development Forum Tokyo Presentation By Vuong Thanh Long Dept. of Economic Development
More informationVolume 37, Issue 2. Modeling volatility of the French stock market
Volume 37, Issue 2 Modeling volatility of the French stock market Nidhal Mgadmi University of Jendouba Khemaies Bougatef University of Kairouan Abstract This paper aims to investigate the volatility of
More informationTHE DYNAMICS OF PRECIOUS METAL MARKETS VAR: A GARCH-TYPE APPROACH. Yue Liang Master of Science in Finance, Simon Fraser University, 2018.
THE DYNAMICS OF PRECIOUS METAL MARKETS VAR: A GARCH-TYPE APPROACH by Yue Liang Master of Science in Finance, Simon Fraser University, 2018 and Wenrui Huang Master of Science in Finance, Simon Fraser University,
More informationEquity Price Dynamics Before and After the Introduction of the Euro: A Note*
Equity Price Dynamics Before and After the Introduction of the Euro: A Note* Yin-Wong Cheung University of California, U.S.A. Frank Westermann University of Munich, Germany Daily data from the German and
More informationA Test of Asymmetric Volatility in the Nigerian Stock Exchange
International Journal of Economics, Finance and Management Sciences 2016; 4(5): 263-268 http://www.sciencepublishinggroup.com/j/ijefm doi: 10.11648/j.ijefm.20160405.15 ISSN: 2326-9553 (Print); ISSN: 2326-9561
More informationAmath 546/Econ 589 Univariate GARCH Models
Amath 546/Econ 589 Univariate GARCH Models Eric Zivot April 24, 2013 Lecture Outline Conditional vs. Unconditional Risk Measures Empirical regularities of asset returns Engle s ARCH model Testing for ARCH
More informationA Study on Developing a VKOSPI Forecasting Model via GARCH Class Models for Intelligent Volatility Trading Systems
지능정보연구제 16 권제 2 호 2010 년 6 월 (pp.19~32) A Study on Developing a VKOSPI Forecasting Model via GARCH Class Models for Intelligent Volatility Trading Systems Sun Woong Kim Visiting Professor, The Graduate
More informationIS GOLD PRICE VOLATILITY IN INDIA LEVERAGED?
IS GOLD PRICE VOLATILITY IN INDIA LEVERAGED? Natchimuthu N, Christ University Ram Raj G, Christ University Hemanth S Angadi, Christ University ABSTRACT This paper examined the presence of leverage effect
More informationTrends in currency s return
IOP Conference Series: Materials Science and Engineering PAPER OPEN ACCESS Trends in currency s return To cite this article: A Tan et al 2018 IOP Conf. Ser.: Mater. Sci. Eng. 332 012001 View the article
More informationThe Economic and Social BOOTSTRAPPING Review, Vol. 31, No. THE 4, R/S October, STATISTIC 2000, pp
The Economic and Social BOOTSTRAPPING Review, Vol. 31, No. THE 4, R/S October, STATISTIC 2000, pp. 351-359 351 Bootstrapping the Small Sample Critical Values of the Rescaled Range Statistic* MARWAN IZZELDIN
More informationA STUDY ON ROBUST ESTIMATORS FOR GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSCEDASTIC MODELS
A STUDY ON ROBUST ESTIMATORS FOR GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSCEDASTIC MODELS Nazish Noor and Farhat Iqbal * Department of Statistics, University of Balochistan, Quetta. Abstract Financial
More informationComovement of Asian Stock Markets and the U.S. Influence *
Global Economy and Finance Journal Volume 3. Number 2. September 2010. Pp. 76-88 Comovement of Asian Stock Markets and the U.S. Influence * Jin Woo Park Using correlation analysis and the extended GARCH
More informationIS INFLATION VOLATILITY CORRELATED FOR THE US AND CANADA?
IS INFLATION VOLATILITY CORRELATED FOR THE US AND CANADA? C. Barry Pfitzner, Department of Economics/Business, Randolph-Macon College, Ashland, VA, bpfitzne@rmc.edu ABSTRACT This paper investigates the
More informationModel Construction & Forecast Based Portfolio Allocation:
QBUS6830 Financial Time Series and Forecasting Model Construction & Forecast Based Portfolio Allocation: Is Quantitative Method Worth It? Members: Bowei Li (303083) Wenjian Xu (308077237) Xiaoyun Lu (3295347)
More informationModelling the stochastic behaviour of short-term interest rates: A survey
Modelling the stochastic behaviour of short-term interest rates: A survey 4 5 6 7 8 9 10 SAMBA/21/04 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 Kjersti Aas September 23, 2004 NR Norwegian Computing
More informationANALYSIS OF THE RETURNS AND VOLATILITY OF THE ENVIRONMENTAL STOCK LEADERS
ANALYSIS OF THE RETURNS AND VOLATILITY OF THE ENVIRONMENTAL STOCK LEADERS Viorica Chirila * Abstract: The last years have been faced with a blasting development of the Socially Responsible Investments
More informationSTOCK MARKET EFFICIENCY, NON-LINEARITY AND THIN TRADING EFFECTS IN SOME SELECTED COMPANIES IN GHANA
STOCK MARKET EFFICIENCY, NON-LINEARITY AND THIN TRADING Abstract EFFECTS IN SOME SELECTED COMPANIES IN GHANA Wiredu Sampson *, Atopeo Apuri Benjamin and Allotey Robert Nii Ampah Department of Statistics,
More informationDoes inflation has an impact on Stock Returns and Volatility? Evidence from Nigeria and Ghana
2011 International Conference on Economics and Finance Research IPEDR vol.4 (2011) (2011) IACSIT Press, Singapore Does inflation has an impact on Stock Returns and Volatility? Evidence from Nigeria and
More informationLecture 6: Non Normal Distributions
Lecture 6: Non Normal Distributions and their Uses in GARCH Modelling Prof. Massimo Guidolin 20192 Financial Econometrics Spring 2015 Overview Non-normalities in (standardized) residuals from asset return
More informationVolatility Spillovers and Causality of Carbon Emissions, Oil and Coal Spot and Futures for the EU and USA
22nd International Congress on Modelling and Simulation, Hobart, Tasmania, Australia, 3 to 8 December 2017 mssanz.org.au/modsim2017 Volatility Spillovers and Causality of Carbon Emissions, Oil and Coal
More informationVOLATILITY OF SELECT SECTORAL INDICES OF INDIAN STOCK MARKET: A STUDY
Indian Journal of Accounting (IJA) 1 ISSN : 0972-1479 (Print) 2395-6127 (Online) Vol. 50 (2), December, 2018, pp. 01-16 VOLATILITY OF SELECT SECTORAL INDICES OF INDIAN STOCK MARKET: A STUDY Prof. A. Sudhakar
More informationThe Analysis of ICBC Stock Based on ARMA-GARCH Model
Volume 04 - Issue 08 August 2018 PP. 11-16 The Analysis of ICBC Stock Based on ARMA-GARCH Model Si-qin LIU 1 Hong-guo SUN 1* 1 (Department of Mathematics and Finance Hunan University of Humanities Science
More informationLinkage between Gold and Crude Oil Spot Markets in India-A Cointegration and Causality Analysis
Linkage between Gold and Crude Oil Spot Markets in India-A Cointegration and Causality Analysis Narinder Pal Singh Associate Professor Jagan Institute of Management Studies Rohini Sector -5, Delhi Sugandha
More informationTHE INFLATION - INFLATION UNCERTAINTY NEXUS IN ROMANIA
THE INFLATION - INFLATION UNCERTAINTY NEXUS IN ROMANIA Daniela ZAPODEANU University of Oradea, Faculty of Economic Science Oradea, Romania Mihail Ioan COCIUBA University of Oradea, Faculty of Economic
More informationEfficiency in the Australian Stock Market, : A Note on Extreme Long-Run Random Walk Behaviour
University of Wollongong Research Online Faculty of Commerce - Papers (Archive) Faculty of Business 2006 Efficiency in the Australian Stock Market, 1875-2006: A Note on Extreme Long-Run Random Walk Behaviour
More informationGARCH Models. Instructor: G. William Schwert
APS 425 Fall 2015 GARCH Models Instructor: G. William Schwert 585-275-2470 schwert@schwert.ssb.rochester.edu Autocorrelated Heteroskedasticity Suppose you have regression residuals Mean = 0, not autocorrelated
More informationA Study on Impact of WPI, IIP and M3 on the Performance of Selected Sectoral Indices of BSE
A Study on Impact of WPI, IIP and M3 on the Performance of Selected Sectoral Indices of BSE J. Gayathiri 1 and Dr. L. Ganesamoorthy 2 1 (Research Scholar, Department of Commerce, Annamalai University,
More informationEconometric Models for the Analysis of Financial Portfolios
Econometric Models for the Analysis of Financial Portfolios Professor Gabriela Victoria ANGHELACHE, Ph.D. Academy of Economic Studies Bucharest Professor Constantin ANGHELACHE, Ph.D. Artifex University
More informationForecasting Value at Risk in the Swedish stock market an investigation of GARCH volatility models
Forecasting Value at Risk in the Swedish stock market an investigation of GARCH volatility models Joel Nilsson Bachelor thesis Supervisor: Lars Forsberg Spring 2015 Abstract The purpose of this thesis
More information2.4 STATISTICAL FOUNDATIONS
2.4 STATISTICAL FOUNDATIONS Characteristics of Return Distributions Moments of Return Distribution Correlation Standard Deviation & Variance Test for Normality of Distributions Time Series Return Volatility
More information